A Noninterleaving Model of Concurrency Based on Transition Systems with Spatial Structure

Abstract

In an attempt to devise a general notion of model for spatial logic, we have been led to consider transition systems with an additional so-called spatial structure on the states, with both the transition and the spatial structures described in coalgebraic terms. In this paper we argue that such transition systems with spatial structure can be seen as a noninterleaving model of concurrency, by providing translations to and from a certain category of Petri nets.

Co-Algebraic Models for Quantitative Spatial Logics

“…This definition, differently from the one in [23], allows us to observe the parallel decomposition of a process only if the involved subprocesses are reactive, i.e. they can synchronize with other processes at some point (similarly to the location semantics of CCS [5]).…”

“…This semantics is inspired both by the STS semantics of [23] and by the location semantics of [5]. A common criticism of spatial logics is that the induced equivalence, in many cases, is too intensional, and coincides with structural equivalence.…”

“…In [23], coalgebras are used to define spatial transition systems (STS), that we extend in this work obtaining SLTS. A STS is made up of a set of states, and two functions that describe respectively the temporal evolution of the system, and the possible parallel decompositions, in a given state.…”

“…In section 3.1, we introduce spatial labeled transition systems (SLTS), a class of coalgebras, reminiscent of spatial transition systems of [23], that extends labeled transition systems with spatial decomposition. Then, in section 3.2, we introduce a logic that is interpreted over SLTS, the quantitative observational spatial μ-calculus (QOS-μ).…”

“…In [16] and [13], for example, spatial logics have been interpreted over particular kinds of graph rewriting systems, rather than on the term language of a specific process calculus. In [23], a non-syntactical interpretation of parallel decomposition is given, by adding spatial information to the semantics of the language: a coalgebraic model, called spatial transition systems (STS), has been developed and tested as a semantic model for a CCS-like process calculus. It has been shown that the STS semantics is fully concurrent (for example, the processes a.b+b.a and a|b have different meanings).…”